RSA-OAEP yields to an RSA encryption scheme providing security against adaptive chosen message attacks (IND-CCA2) in the random oracle model, while plain RSA does not even provide IND-CPA security.

If you mean security (which I assume), then yes, ECIES also achieves the same formal security guarantees as RSA-OAEP in the elliptic curve setting.

If you want an encryption scheme for elliptic curves providing IND-CCA2 security without random oracles, i.e., relying only on standard assumptions, then you can take the elliptic curve version of Cramer-Shoup encryption.

Latter however, is less efficient then ECIES.

If you only require IND-CPA security, you can also use elliptic curve versions of ElGamal encryption.

Finally, while ECIES is a hybrid encryption scheme by design, the others aren't. However, you can turn them into hybrid schemes.